Derive de-Broglie equation.

Explanation

`implies` de-Broglie combined the following two equations of energy of which one represents wave character `(hv)` and the other represents the particle nature `(mc^2)`.
(i) Planck.s quantum hypothesis : E = hv
(ii) Einsteins mass-energy relationship :
`E = mc^2`
From (i) and (ii)
`hv = mc^2`
`hv = mc^2`
`hc//lambda = mc^2`
`lambda = h//mc`
`implies` The equation represents the wavelength of photons whose momentum is given by mc (Photons have zero rest mass)
`implies` For a particle of matter with mass m and moving with a velocity v, the equation can be written as
`lambda = h//mv`
`implies` This is valid only when the particle travels at speeds much less than the speed of light.